FISHERY BULLETIN: VOL. 86, NO. 1 



fish stock dynamics need much more rigorous es- 

 timates of within-stock variability (both trends 

 and variance) in M for exploited fish stocks. 



II. CURRENT METHODS FOR 

 ESTIMATING NATURAL MORTALITY 



Three methods are used currently or have been 

 proposed to estimate M in fish populations: 

 1) analysis of catch data, usually from commer- 

 cial fisheries but also from sampling programs 

 specifically conducted for stock assessment (this 

 includes mark-recapture studies), 2) correlations 

 of M with other life history parameters, and 

 3) estimation of deaths due to predation. I de- 

 scribe below each method in turn, listing both 

 advantages and disadvantages of each. 



Catch-Analysis Methods 



Methods for deriving estimates of natural mor- 

 tality from catch data are based on measuring 

 decreases in abundance, either relative or abso- 

 lute, in groups of fish during two or more succes- 

 sive periods of time. Groups may be distinguished 

 on the basis of any identifiable characteristic, 

 e.g., size (length or weight), age, sex, location and 

 time of capture, or some identifiable tag or mark. 



The most common grouping is by age, for two 

 reasons. First, age has been considered histori- 

 cally the most important factor potentially affect- 

 ing estimates of mortality rate and subsequent 

 results from the most commonly used fishery 

 models (e.g., Heincke 1913; Baranov 1918). This 

 is probably because the methods were developed 

 for temperate water fisheries which tend to have 

 obvious annual reproductive cycles, so that indi- 

 vidual year classes are often relatively easy to 

 distinguish. Second, the earliest method of esti- 

 mating M (catch curve analysis, discussed below) 

 depends on determining the rate during succes- 

 sive ages. 



Regardless of the grouping criterion, methods 

 for estimating M use generally one of two types of 

 data. The first type is simply subsamples of un- 

 marked catch. These subsamples contain fish se- 

 lected randomly and classified into groups on the 

 basis of size (length or weight). The second type is 

 mark-recaptures, in which previously marked in- 

 dividual fish can be identified and classified after 

 recapture into groups on the basis of this positive 

 identification. Estimates of mortality are usually 

 derived from samples of unmarked fish by analy- 

 sis of resulting "catch curves" (Ricker 1975). Be- 



cause it has been used so frequently, catch curve 

 analysis is discussed below in some detail. 



With marking it is possible to follow the history 

 of individual fish, so many different types of esti- 

 mation procedures exist for deriving estimates of 

 mortality from mark-recapture data (e.g., Ricker 

 1975; Jones 1979; Brownie et al. 1985). Because 

 so many variations are possible, marking experi- 

 ments are discussed only generally, stressing 

 the basic advantages and disadvantages of mark- 

 ing data relative to data from unmarked samples, 

 in deriving estimates of mortality from these 

 data. 



Size-frequency distributions from unmarked 

 subsamples of catch (the first type of data) are 

 converted usually to age-frequency distributions, 

 on the basis of previously determined relation- 

 ships between age and length or age and weight. 

 Subsequent analyses concentrate on analyzing 

 this resulting curve of age-composition (e.g., 

 Ricker 1975). Abundance usually decreases expo- 

 nentially with size (or age) in this type of sample. 

 Converting the abundances to their logarithmic 

 values often results in a relatively linear decrease 

 during most exploited ages (or sizes), after some 

 initial increase in vulnerability. Graphs of these 

 logged-frequency distributions are usually called 

 "catch curves", and their analysis, "catch curve 

 analysis". "Catch curve analysis" generally con- 

 sists of determining the best-fit straight line 

 through the decreasing portion of the logged- 

 frequency distribution, because if the decrease in 

 abundance is truly exponential, the slope of this 

 line through the log-transformed data is the in- 

 stantaneous rate of decrease in abundance (e.g., 

 Ricker 1975). 



There are two basic t3T)es of catch curves, dis- 

 tinguished on the basis of when the data were 

 collected and how many groups are represented in 

 the curves. The first, horizontal catch curves, in- 

 cludes data from several groups (e.g., size or age 

 classes) collected at a single point in time (or com- 

 bined from two or more points in time). Thus, 

 horizontal catch curves reflect "ancient history". 

 The individuals contributing to the frequency dis- 

 tribution were not originally all members of the 

 same group. To use this type of catch curve, one 

 must assume that for each successive age, risk of 

 mortality has been historically the same for all 

 individuals achieving that age. If this has not 

 been the case, the catch curves may show various 

 types of curvature in the descending leg, but ab- 

 sence of curvature is no guarantee that the rates 

 have in fact been constant. 



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